You can't easily use an old Windows 7 disk in a new computer.
Apart from the problem of drivers, you will also need to re-activate Windows, as too much hardware will have changed. And as your serial number is already taken for the old computer, you will have to beg Microsoft on the phone for a new serial. And if your current serial is OEM, then you can forget the whole thing right now.
You will need to reinstall Windows. See How to Run a Startup Repair in Windows 7 for how to do that in a way that preserves the existing applications.
Just remember that once that is done, you will find yourself starting the Windows trial period. I just hope that as in your case this is an old installation, Windows might not decide that the trial period is over and lock you out until you can supply a new serial.